Kernel PCA Contour Maps for Fault Detection

Visualizations of the T2 and Q statistical indices for KPCA-based fault detection using contour maps

This submission contains the following files:
1) dataset.mat
2) KPCAsurface.m
3) PCAsurface.m
4) greenmag.m

dataset.mat contains a 2-dimensional data set taken from a simulated process example. This data is used for training and testing Kernel PCA for fault detection. After training, the widely used T2 and Q statistical indices for fault detection are computed for every location in the output data space, hence producing contour maps. The 99% significance level detection limit is then superimposed on the map, serving as a boundary between the normal (green) and faulty (magenta) regions of the data space.

Using the contour maps, one can visualize the effects of various kernel types and parameter choices to the decision boundary between normal and faulty process states.

This work is supplementary to the results in Ref [1]. Further work can proceed by investigating the impact of kernel behavior to process monitoring performance.

[1] K.E.S. Pilario, Y. Cao, and M. Shafiee. Mixed Kernel Canonical Variate Dissimilarity Analysis for Incipient Fault Monitoring in Nonlinear Dynamic Processes. Comput. and Chem. Eng., 123, 143-154. 2019. doi: 10.1016/j.compchemeng.2018.12.027